To give a good answer to this one, we've got to start out with some
physics. Some of this might be a repetition of what you've already
learned, so I'll try to keep the review part a bit short!

Each color of light has a distinct wavelength, with blue and violet being
the shortest and red being the longest. As the wavelength gets shorter,
the amount of energy in the light increases. One way to think about it
is to think of making waves by shaking a rope - you have to work a lot
harder to make a lot of short waves than to make just a few lazy, long
waves. UV is even shorter in wavelength than blue and violet, so it
packs even more energy.

The energy required to make a photon with a given wavelength increases,
too, as the wavelength gets shorter. This makes sense - if a photon
packs more energy in it, then it must take more energy to make it. So
then we think of ways to make things more energetic, and we come up with
temperature. As an object heats up, it is able to make ever-shorter
wavelengths of light. That's why things go from being red-hot to yellow-
hot to white-hot. We see this in heated metal, electric lights, and in
stars. Which takes us to the sun.

Any heated object will give off light, and the color of that light
depends on the temperature of the object, as we just went over. However,
a hot object will give off a number of wavelengths. Sunlight, for
example, can be broken down into many colors - just as we see in a
rainbow. The reason the sun looks yellow is because, for the sun's
temperature, the spectrum peaks in yellow - there are more yellow photons
given off than other colors. So the sun looks yellow. Shorter
wavelengths (including UV) are there, it's just that there isn't much
because the sun is too cool to make much UV. Which brings us directly to
your question. A lot of this was discovered by Max Planck almost a
century ago.

Each color has its own distinctive wavelength; UV is often taken to have
a band of 100 - 400 nm (a billion nm makes 1 meter). So what we have to
do is to add up the energy that reaches the earth's surface in this
wavelength band and figure out what fraction of all solar energy this
is. The fraction varies from day to day because of changes in the angle
the sunlight makes and "stuff" in the atmosphere that can absorb UV.
Ozone absorbs a lot of UV, as does water vapor, so a desert location may
have higher UV levels than someplace on the water. When the sun is
directly overhead, the light shines straight down through the atmosphere,
so it passes through less air and has more UV in it.

So - given all that, here's the scoop. As an average, we see about 1/2
milliwatt (mW) of UV radiation per square cm of surface area at sea level
in the temperate zone (such as most of the US). By comparison, the
average amount of total solar radiation reaching the earth's surface is
about 100 mw per square cm, so the fraction of this that is UV is about
0.5%.

However, this number depends critically upon what you are measuring! If
you are comparing UV to visible light reaching the earth's surface, you
will get a much different (smaller) number than if you're looking at
TOTAL solar energy reaching the earth. Although the tanning salon is no
doubt using a single UV wavelength band (UVA), this makes up most of the
UV reaching the earth's surface.

So the short version is that the amount of UV radiation (wavelength
between 100 and 400 nm) reaching the earth's surface is about 0.5% of
the total amount of solar radiation reaching the earth's surface. This
is a lot less than what the tanning salon has.

Finally, I've got to advise against using a tanning bed at all. The
risks of tanning are fairly well-known and include premature aging of the
skin (the skin turns leathery and wrinkled faster) and skin cancer.
There are many advisories about this, including this one issued by the
Health Physics Society.